There are two boxes A and B. In box A, there are 3 red marbles and 5 green marbles. In box B, there are 2 red marbles and 3 green marbles. Jack rolls the dice. If the result is 1 or 6 then Jack will pick a marble from box A. If the result is neither 1 nor 6 then Jack will pick a marble from box B. What is the probability that the picked marble is green?
A. 1/8
B. 73/120
C. 21/40
D. 5/24
E. 25/56
The OA is B .
Experts, may you assist me here? I don't know how to solve this question. I would be thankful.
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There are two boxes A and B. In box A, there are 3 red . . .
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EconomistGMATTutor
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Hi VJesus12,There are two boxes A and B. In box A, there are 3 red marbles and 5 green marbles. In box B, there are 2 red marbles and 3 green marbles. Jack rolls the dice. If the result is 1 or 6 then Jack will pick a marble from box A. If the result is neither 1 nor 6 then Jack will pick a marble from box B. What is the probability that the picked marble is green?
A. 1/8
B. 73/120
C. 21/40
D. 5/24
E. 25/56
The OA is B .
Experts, may you assist me here? I don't know how to solve this question. I would be thankful.
Let's take a look at your question.
P(Box A) = 2/6 = 1/3
P(Green marble from Box A) = 5/8
P(Box A) and P(Green marble from Box A)
$$=\frac{1}{3}\times\frac{5}{8}=\frac{5}{24}$$
P(Box B) = 4/6 = 2/3
P(Green marble from Box B) = 3/5
P(Box B) and P(Green marble from Box B)
$$=\frac{2}{3}\times\frac{3}{5}=\frac{2}{5}$$
We are asked to find the probability that the picked marble is green.We know that the green marble can be selected from either Box A or Box B. Therefore,
= P(Box A) * P(Green marble from Box A) + P(Box B) * P(Green marble from Box B)
$$=\frac{5}{24}+\frac{2}{5}$$
$$=\frac{25+48}{120}=\frac{73}{120}$$
Therefore, Option B is correct.
Hope it helps.
I am available if you'd like any follow up.
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harshitpuri
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this is a question related to probability
you have to calculate probabilty of green marble from a as well as b and add them.
Probability that A bag is chosen = (1,6)=1/3
probability of green marble from A = 5/8 (green / total)
probabiluty combined a and green matble from A= (1/3 )x (5/8)......(i)
Probability that B bag is chosen = (2,3,4,5)=2/3
probability of green marble from A = 3/5 (green / total)
probabiluty combined a and green matble from B= (2/3 )x (3/5)......(ii)
Add i and ii u will get ans 73/120...B
you have to calculate probabilty of green marble from a as well as b and add them.
Probability that A bag is chosen = (1,6)=1/3
probability of green marble from A = 5/8 (green / total)
probabiluty combined a and green matble from A= (1/3 )x (5/8)......(i)
Probability that B bag is chosen = (2,3,4,5)=2/3
probability of green marble from A = 3/5 (green / total)
probabiluty combined a and green matble from B= (2/3 )x (3/5)......(ii)
Add i and ii u will get ans 73/120...B
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We are given that in box A, there are 3 red marbles and 5 green marbles, and in box B, there are 2 red marbles and 3 green marbles. When the die is rolled, if the result is 1 or 6 then Jack will pick a marble from box A, and if the result if neither 1 nor 6 then Jack will pick a marble from box B. We need to determine the probability that a green marble is selected.VJesus12 wrote:There are two boxes A and B. In box A, there are 3 red marbles and 5 green marbles. In box B, there are 2 red marbles and 3 green marbles. Jack rolls the dice. If the result is 1 or 6 then Jack will pick a marble from box A. If the result is neither 1 nor 6 then Jack will pick a marble from box B. What is the probability that the picked marble is green?
A. 1/8
B. 73/120
C. 21/40
D. 5/24
E. 25/56
Notice that the probability that a green marble is selected is the probability that a green marble is selected from box A or from box B. That is, the probability of selecting a green marble is the probability that it's selected from box A plus the probability that it's selected from box B. Let's start with box A.
P(rolling a 1 or 6) = 2/6 = 1/3
P(selecting a green marble) = 5/8
Thus, the probability of selecting a green marble from box A is 1/3 x 5/8 = 5/24.
Now we can move to box B.
P(not rolling a 1 or 6) = 2/3
P(selecting a green marble) = 3/5
Thus, the probability of selecting a green marble from box B is 2/3 x 3/5 = 2/5.
The probability of selecting a green marble from box A or box B is:
5/24 + 2/5 = 25/120 + 48/120 = 73/120
Answer: B
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